Physics Waves UHS 2023
PMDC Verified Question 29 of 125
If the length of second pendulum becomes four times, then its time period will become:
A
Four times
B
Two times
C
Half
D
One fourth
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: Two times
Concept:

The time period of a simple pendulum is directly proportional to the square root of its length.

Formula:

$$ T = 2\pi \sqrt{\frac{L}{g}} $$

Solution:

  • The original time period \( T \propto \sqrt{L} \).


  • If the new length \( L_{new} = 4L \), substitute it into the relation: \( T_{new} \propto \sqrt{4L} \).


  • Extract the constant: \( \sqrt{4L} = 2\sqrt{L} \).


  • Therefore, the new time period is exactly two times the original (\( T_{new} = 2T \)).


Why other options are incorrect:

Option A (four times) incorrectly assumes the period scales linearly with length. Option C (half) occurs if one mistakenly divides by the square root.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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